A318676 Sum of divisors of n that have an even number of prime factors (counted with multiplicity).

1, 1, 1, 5, 1, 7, 1, 5, 10, 11, 1, 11, 1, 15, 16, 21, 1, 16, 1, 15, 22, 23, 1, 35, 26, 27, 10, 19, 1, 32, 1, 21, 34, 35, 36, 56, 1, 39, 40, 55, 1, 42, 1, 27, 25, 47, 1, 51, 50, 36, 52, 31, 1, 70, 56, 75, 58, 59, 1, 96, 1, 63, 31, 85, 66, 62, 1, 39, 70, 60, 1, 80, 1, 75, 41, 43, 78, 72, 1, 71, 91, 83, 1, 130, 86, 87, 88, 115, 1, 131, 92, 51

Offset: 1

Author

Antti Karttunen, Sep 04 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A008836, A065043, A318674, A318677.

Cf. also A038548, A066839.

Programs

Mathematica

Array[DivisorSum[#, # &, EvenQ@ PrimeOmega@ # &] &, 92] (* Michael De Vlieger, Sep 04 2018 *)

PARI

A318676(n) = sumdiv(n,d,(!(bigomega(d)%2))*d);

Formula

a(n) = Sum_{d|n} [A008836(d) > 0]*d.

a(n) = A000203(n) - A318677(n).

For all n >= 1, a(n) >= A318674(n).

a(n) = Sum_{d|n} d*A065043(d). - Antti Karttunen, Jan 24 2024